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Full text of "Analytical Mechanics"

MOTION                                       77
the pound (weight) by its usual abbreviation we have 2.205 Ibs. = the weight of 1000 gms.*
VELOCITY.
77.   Displacement.  When the position of a particle with respect to a reference system is slightly changed it is said to  have  been  displaced, and the
vector s, Fig. 46, which has its origin at the initial position and its terminus at the final position, is called a displacement
78.   Velocity. If a particle undergoes   equal   displacements   in equal intervals of time, however
p
small these intervals, it is said to               FlG 46
have a constant velocity.    In this
particular case the velocity equals, numerically, the distance covered per second. When, therefore, a distance 5 is covered in an interval of time l} the velocity is given by
_ s
By equal displacements are meant displacements equal in magnitude and the same in direction. Therefore constant velocity means a velocity which is constant in direction as well as in magnitude. The magnitude of velocity without regard to its direction is called speed.
In general, bodies not only cover unequal distances in equal intervals of time, but also change their directions of motion. Therefore we need a definition of velocity like the following, which is perfectly general.
Tlie velocity of a particle at any point of its path equals, in magnitude, the lime rate at which it describes that part of the path which is in the immediate neighborhood of the point and has the direction of the tangent at that point.
* For the relation between mass and weight see p. 109.